Rituximab is a man-made antibody used to treat certain types of cancer. This study will determine whether rituximab is an effective treatment for adult and pediatric patients with dermatomyositis or polymyositis. Study hypotheses: 1) The time to improvement in Group A patients (receiving rituximab first) will occur significantly earlier than in Group B patients (receiving rituximab later). 2) The proportion of patients improved at Week 8 of the treatment phase will be significantly greater in Group A compared with Group B. Rituximab is a chimeric, murine-human, genetically engineered monoclonal antibody directed against the CD20 antigen found on the surface B-lymphocytes and is known to deplete B cells when administered intravenously. It is approved to treat non-Hodgkin's lymphoma. Rituximab has been used for autoimmune diseases such as systemic lupus erythematosus (SLE), rheumatoid arthritis (RA), and immune-mediated hematologic disorders. It has also been studied and used in small numbers of patients with myositis. This study will evaluate the efficacy of rituximab in treating refractory adult and pediatric patients with dermatomyositis and adult polymyositis. A patient's participation in this study will last approximately 45 weeks. At screening, participants will have a physical exam, muscle strength assessment, an electrocardiogram, and blood and urine collection;they will also be asked to complete several questionnaires. All participants will receive 2 infusions of rituximab and 2 infusions of placebo. Participants will be randomly assigned to one of two groups. Group A will receive rituximab at Weeks 0 and 1 and placebo at Weeks 8 and 9. Group B will receive placebo at Weeks 0 and 1 and rituximab at Weeks 8 and 9. Each infusion will be given on an outpatient basis over a minimum of approximately 5 hours'time. There will be a total of 14 study visits. All participants will visit the outpatient clinic at selected time points for muscle strength testing, a physical exam, disease activity measurements, and blood collection. During the study, participants will be monitored closely for improvement or worsening of their disease and for serious drug related side effects. Some participants will be asked if they are willing to undergo 2 muscle biopsy procedures, 1 prior to receiving study medication and 1 after receiving study medication, to determine the effects of rituximab on muscle tissue.